Definition:Fibonacci Prime Pair

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Theorem

A Fibonacci prime pair is a pair of Fibonacci numbers $F_p$ and $F_{p + 2}$ such that:

$p$ and $p + 2$ are both prime numbers
$F_p$ and $F_{p + 2}$ are both prime numbers.


Examples

The only known examples of Fibonacci prime pairs are:

$\tuple {F_5, F_7}, \tuple {F_{11}, F_{13} }, \tuple {F_{431}, F_{433} }, \tuple {F_{569}, F_{571} }$

This sequence is A073340 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Sources